The BICEP2 collaboration reports a B-mode polarization of the cosmic microwave background (CMB) radiation inconsistent with the null hypothesis at a significance of > 5 sigma . This recent and potentially important result is being often interpreted as a signature of primordial gravitational waves from cosmic inflation. However, the arguments supporting such an interpretation are strictly based on standard cosmology and do not take into account possible new phenomena suggested by Planck data such as the existence of a privileged space direction. In particular, inflation is not needed in pre-Big Bang patterns, and the spinorial space-time (SST) introduced in our 1996-97 papers automatically generates a privileged space direction for each comoving observer. In the presence of this privileged space direction, the existence of CMB B-modes is a natural phenomenon and the signal claimed by BICEP2 would not correspond to any kind of inflationary scenario.